While Republican tensions over tackling the national debt have been on public display for days, Democrats have also been squabbling with one another, though largely out of view.

At issue for Democrats is whether the party risks going overboard in its embrace of tax increases — a perilous proposition for lawmakers from political battlegrounds.

Those tensions erupted at a private meeting this week of a handful of key Democratic members.

Sen. Bill Nelson (D-Fla.), facing reelection next year, spoke up to oppose a plan being drafted by Senate Budget Committee Chairman Kent Conrad that would impose a new surtax on millionaires of about three percent on top of the higher tax rates they would face when the George W. Bush tax cuts expire next year, according to several people familiar with the exchange.

Nelson later explained through a spokesman that he was opposed to “double taxation,” even on the wealthy.

Another centrist on the budget committee, Sen. Mark Begich (D-Alaska), has also opposed the idea.

Several centrist Democrats have been voicing concern in private sessions that Conrad’s draft may be shifting too far to the left in order to placate liberals on the committee whose votes are needed to move the legislation, according to aides.

Republicans have been rallying around a House spending plan authored by Budget Committee Chairman Paul Ryan (R-Wis.), even as they’ve been sending mixed signals in recent days over a key provision calling for a deep overhaul of Medicare.

The Democratic-run Senate, meantime, has been unable — or unwilling — to lay out its alternative agenda.

The fracturing within the party illustrates the political dilemma facing Democrats as budget negotiations and the 2012 election cycle heat up simultaneously.

Democrats say they are committed to reducing the deficit, but they vehemently oppose many of the cuts spelled out by the House GOP. That means raising taxes — which could leave some Democrats vulnerable to the old tax-and-spend label that has long haunted the party in competitive elections. The big question roiling Democratic ranks: How much deficit reduction are they — and the voters — willing to accept in the form of higher taxes?

Republicans, urged on by their tea party base, say any tax increase is a non-starter — and the GOP is preparing to target centrist Democrats such as Nelson for their support of tax hikes.

“There are folks in both caucuses who have drawn lines in the sand,” said Sen. Chris Coons (D-Del.), a budget committee member. “Getting them to agree to get past that and to move forward with proposals that have everything on the table is quite challenging.”

Still, Coons said it was important for Senate Democrats to reach a consensus on a budget plan as a marker for bipartisan negotiations, to “show a competing vision.”

Many Democrats were uneasy about the recommendations last year from the bipartisan fiscal commission appointed by President Obama, which called for $4 trillion in deficit reduction over a decade. Obama laid out his own framework last month that he said would realize about $4 trillion over 12 years.

But some liberal Democratic senators worry that Obama, who needs swing voters for next year’s election, is prepared to rely too much on spending cuts and not enough on higher taxes to achieve the deficit reduction. They view a Senate budget plan as a way to pull negotiations leftward as bipartisan talks intensify in the coming days.

Conrad, trying to balance the conflicting ideologies and political concerns of his caucus colleagues, has found himself shuttling between Democratic factions in recent days — selling ideas, hearing complaints, tweaking his draft and tweaking it again. Whether it’s raising taxes or slashing spending, Democrats across the ideological spectrum have been anxious.

“This is hard political medicine,” said Maya MacGuineas, president of the bipartisan Committee for a Responsible Federal Budget.

“There’s been a void of the Democratic voices saying how they would fix the situation,” MacGuineas added. “Paul Ryan has been out there on the right putting out the Republican specifics, and the fiscal commission has shown a bipartisan approach, but there hasn’t really been a true Democratic plan for people to rally around.”

The millionaires tax was pushed by Sen. Bernie Sanders, (I-Vt.), a socialist and a member of the budget committee. He initially called for a 5.4 percent surtax on adjusted gross incomes over $1 million, which Sanders said would raise as much as $50 billion a year.

People familiar with the Democrats’ discussions say Conrad is considering a three-percent millionaires surtax.

Sanders, in an interview, waved off criticisms of the surtax, saying its inclusion would help Democrats’ campaigns — including his own.

“I’m running for reelection, and I think this is what the American people want,” he said. ”Asking the wealthiest people in this country to contribute to deficit reduction is not only good policy, it’s good politics.”

Asked by reporters about the inclusion of the millionaires surtax, Conrad cautioned Wednesday that he could not yet say what the Democratic plan would entail.

“Nothing’s final until everything’s final,” he said. “Things that might be in a draft or were up for discussion may or may not be there at the finish line.”

Conrad, who is also immersed in bipartisan talks with the so-called Gang of Six, told his fellow Democrats this week that his budget plan would cut the deficit by $4 trillion over 10 years. Senate Majority leader Harry Reid (D-Nev.) said this week that half of the reductions would come from tax increases and half from spending cuts — but experts warn that such ratios can be misleading without additional data.

Reid, meantime, has told his caucus to move cautiously before embracing any budget plan. “There are a lot of things floating around here,” he said last week. “And I told my members just — let’s not be signing onto all this stuff until we really know where we’re headed.”

An additional point of tension among Democrats over the budget was on display this week when Sens. Mary Landrieu (D-La.) and Begich used a Senate floor back-and-forth to lampoon a proposal by party leaders to eliminate billions of dollars in tax subsidies for big oil companies. Oil is an important home-state industry for both senators. Reid and other top Democrats say the savings should go toward deficit reduction.

Begich accused his fellow Democrats of “going for headlines” in hauling oil executives to the Capitol this week for hearings. Landrieu called it a “gimmick” to push for an end to the subsidies.

“It’s laughable,” she said.